I haven't heard anything lately, but in 2005-07 there was some talk at a couple of South Bay's Board meetings about the possibility. At the time it was said that RBFD had expressed some interest in pursuing the idea, but that the police chief had no interest in it at all.
From their 1/23/2007 Board of Directors, Executive Committee and User Committee Meeting minutes (no longer online, that I can find):
"Executive Director Mailloux related the Redondo Beach Fire Department’s request to use one of the Authority’s UHF radio frequencies for interoperability purposes.
"[Manhattan Beach Fire] Chief Groat explained that, during emergencies that require mutual aid, Redondo Beach has been isolated from other South Bay cities because of the frequency on which they have been operating. He pointed out that it would be good to further populate the Authority’s Fire Tactical 2 UHF frequency and that, according to Chief Madrigal’s letter of December 7, 2006, Redondo Beach offered to pay to use it. It was Chief Groat’s feeling that, even if it means charging them, Redondo Beach Fire Department should be permitted to operate on one of the Authority’s UHF frequencies during emergencies that require mutual aid.
"Noting that he and [MB] City Manager Dolan gave the Redondo Beach City Manager a tour of the Authority’s facility a few months ago, [Hermosa Beach] City Manager Burrell pointed out that this could be an opportunity to begin discussions about the Authority providing Redondo Beach’s 9-1-1 dispatching services.
"Executive Director Mailloux stated his impression that Redondo Beach’s Police Chief has no interest in returning to the Authority.
"City Manager Dolan observed that an opportunity to provide 9-1-1 dispatching services to the Redondo Beach Police Department is probably down the road when their current Police Chief leaves. He agreed to the idea of approving the Redondo Beach Fire Department’s request with the caveat that they pay for it."
I don't know if the players, especially the Redondo COP, are still the same or if there's been any movement since then. South Bay's original dispatch center was at RBPD - in the windowless, stuffy basement that was their old pistol range, but Redondo quit in 1983 and the "RCC" moved to a former school administration building in Hawthorne until they built their current center next door to Hawthorne PD.